Measurement noise refers to the random and unpredictable fluctuations superimposed on the useful signal during a measurement, limiting the precision of the result obtained.
Discover FizziQ
How to measure it in class
With the FizziQ app, it is easy to visualize the measurement noise of a smartphone sensor.
Steps:
- Open FizziQ and select the acceleration sensor. Place the smartphone perfectly flat on a stable table and start a 30-second recording.
- Observe the recorded data: even when stationary, the sensor displays small variations around the expected theoretical value (g ≈ 9.81 m/s²).
- Calculate the mean and the standard deviation of the recorded values. The standard deviation represents the sensor’s noise level.
- Repeat the experiment by placing the smartphone on a less stable surface (for example on a book placed on top of another). Compare the noise levels and discuss the influence of the environment.
Scientific activities on this topic
Several experiments that are easy to carry out with a smartphone, a tablet or a computer allow you to observe and quantify sensor measurement noise.
- 1: Evaluate the quality of a sensor - Analysis of a sensor’s precision
- 2: White noise - What frequencies make up white noise?
- 3: Uncertainty - Analyzing measurement uncertainties
Learn more
The different types of noise
In physics, several types of noise are distinguished. White noise has the same intensity at all frequencies, like the hiss of a radio. Pink noise, or 1/f noise, is more intense at low frequencies and appears in many natural phenomena. Shot noise is related to the discrete nature of electric charges. Each type of noise has different statistical properties.
Johnson-Nyquist thermal noise
In 1928, John B. Johnson measured and Harry Nyquist modeled the noise generated by the thermal agitation of electrons in a conductor. This noise, proportional to the temperature and to the resistance of the conductor, constitutes a fundamental limit for any electronic measurement. At room temperature (300 K), a 1 kΩ resistor generates a noise of approximately 4 nV/√Hz.
Noise reduction techniques
Several methods make it possible to reduce the impact of noise. Time averaging reduces noise as 1/√n. Low-pass filtering eliminates the high-frequency components of the noise. Lock-in detection makes it possible to extract a periodic signal buried in noise a thousand times more intense. In astronomy, space telescopes eliminate atmospheric noise.
Orders of magnitude of noise
The noise of a smartphone MEMS accelerometer is typically 0.003 to 0.01 m/s². The noise of a barometric pressure sensor is approximately 0.01 to 0.05 hPa. The human hearing threshold (0 dB SPL) corresponds to an acoustic pressure of only 20 µPa, barely above the thermal noise of air.
Formula
The signal-to-noise ratio (SNR) quantifies the quality of a measurement:
SNR = 20 × log₁₀(A_signal / A_noise)
Meaning: SNR: signal-to-noise ratio (in decibels, dB) A_signal: amplitude of the useful signal A_noise: amplitude of the noise log₁₀: base-10 logarithm
Application examples
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The background hiss audible when you turn up the volume of headphones without music playing
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The small brightness fluctuations visible in a photo taken in low light
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The oscillations of the weight displayed by a precision scale placed on an unstable table
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The twinkling of stars caused by atmospheric turbulence
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The static on an FM radio when the signal is weak
FAQ
Q: Can measurement noise be completely eliminated? A: No, noise is inherent to any measurement system. It can be reduced through averaging, filtering or improving the measurement environment, but never completely eliminated.
Q: How can you distinguish noise from a real signal? A: If the fluctuations are random and disappear when averaging many measurements, it is noise. A real physical signal persists after averaging and often shows a recognizable pattern.
Q: Is noise the same for all sensors in a smartphone? A: No. Each sensor has its own noise level, which depends on its technology and quality. The pressure sensor is generally less noisy than the accelerometer.
Q: Why does averaging reduce noise? A: Noise is random: its positive and negative values tend to cancel out when averaging. The useful signal, however, remains constant. Noise decreases as 1/√n, where n is the number of measurements averaged.
Q: Does noise increase with temperature? A: Yes, the thermal noise (Johnson noise) of electronic components increases with temperature. In practice, this effect is small at classroom temperatures.
Related concepts
Standard Deviation - Precision - Resolution - Systematic vs Random Error